The present invention relates to digital signal transmission, and in particular, relates to transmission line filters having both low-reflection and Gaussian amplitude characteristics.
In digital signal transmission, Gaussian-like frequency-domain transfer functions are often desirable because they effectively cut off high frequency components and do not yield overshoots and ringing in the time domain. A well-known example of a filter that has such functional characteristics is the Bessel-Thomson filter. These filters have been used in microwave range transmission in lumped-element and transmission-line design configurations.
Bessel-Thomson filters are theoretically lossless since they do not incorporate resistive elements and they provide for a maximally flat group delay. Even in practical implementations in which some amount of electrical resistance is inevitable, the magnitude of the transmission transfer function in the passband for such filters (|s21|=|s12|) is close to 1 (0 dB) and the magnitude of the reflection coefficient (|s11|=|s22|) is close to 0. The filters have a mild transition from the passband to the stopband, where the magnitude of the transfer function and reflection coefficients reverse, with the transfer function dropping to approximately zero, and the reflection coefficient rising to approximately 1. Thus, in the stopband, the Bessel-Thomson filter acts approximately as a pure reflector, which is an undesirable effect for many digital communication applications.
The present invention provides a transmission line filter having low reflectivity and Gaussian characteristics that includes at least one inductive element aligned along the transmission line and at least one shunt configuration branching off the transmission line including a capacitive element and a resistive element. In accordance with one embodiment, the capacitive element and the resistive element are in series in the at least one shunt configuration.
According a particular embodiment, the at least one inductive element, the capacitive element, and/or the resistive element are distributed parameters which are spread evenly over the transmission line.
According to a further embodiment, the present invention provides a complete Gaussian transmission line filter that includes at least one resistive element aligned in the direction of transmission parallel to the at least one inductive element.
The present invention also provides a complete Gaussian transmission line filter in which the line parameters are configured as lumped elements. According to this embodiment, the transmission line filter includes a discrete number (N) of half-cell sections distributed in series along the transmission line, each half-cell section further including an inductive element (l) and a resistive element (r) in parallel and aligned in a direction of transmission, and a resistive element (g) and a capacitive element (c) in series and aligned in a shunt configuration branching from the transmission line.
According to further embodiment, the present invention provides an incomplete Gaussian transmission line filter that includes a number (N) of half-cell sections distributed in series along the transmission line, each half-cell section including: a) an inductive element (l) aligned in the direction of transmission; and b) a resistive element (g) and a capacitive element (c) in series and aligned in a shunt configuration branching from the transmission line.
The present invention also provides a topology for modeling a transmission line filter having low reflectivity and Gaussian characteristics. The topology includes a ladder network having both a plurality of inductive elements aligned in series along a direction of transmission, and a plurality of shunt branches coupled to the inductive elements and aligned away from the direction of transmission, each shunt branch having a capacitive element and a resistive element coupled in series. The topology is used to generate parameter values for the inductive, and capacitive and resistive elements for achieving specified filter characteristics.
According to one embodiment, the ladder network includes a plurality of resistive elements aligned in series along the direction of transmission, parallel to the plurality of inductive elements.
According to a particular embodiment, the plurality of inductive elements, the plurality of capacitive elements, and the plurality of resistive elements are modeled as being distributed per unit length over the transmission line.
According to a further embodiment, the ladder network includes a number of (N) half-cell sections including a first end half-cell section, a second end half-cell section, and intermediate half-cell sections. Each half-cell section includes one inductive element and one shunt branch, values for the inductive, capacitive and resistive elements within all intermediate half-cells being identical.
The present invention also provides a method of designing a transmission line filter having low reflectivity and Gaussian characteristics, in which the transmission line filter includes a number of half cells, each half cell having an inductive element aligned along the transmission line, and a shunt branch off of the transmission line, the shunt branch having a capacitive and a resistive element in series. The method includes ascertaining values for desired filter parameters, deriving formulas for the values of the inductive, capacitive and resistive elements in terms of the desired filter parameters and the number of half-cells, selecting a number of half-cells for the filter required to achieve the desired filter parameters, and estimating lumped element values for the inductive, capacitive, and resistive elements using the selected number of half-cells.
According to a particular embodiment of the method of the present invention, the inductive, capacitive, and resistive elements of the transmission line are modeled as distributed line parameters prior to deriving the formulas for the values of the elements.
According to a further embodiment, the estimated values for the lumped element values are optimized using a circuit simulator.
According to a further embodiment, the number of half-cells is selected to provide a cutoff frequency for the filter above a threshold level.
According to a further embodiment, the number of half-cells are selected in order to obtain the optimized lumped element values and the number of half-cells selected is approximated as an integer value.
According to a particular implementation of the method of the present invention directed to achieving highly linear phase characteristics, a cutoff frequency for the filter is recomputed, the lumped element values are re-estimated using the recomputed cutoff frequency, and the lumped element values using the circuit simulator are re-optimized.
The present invention also provides for implementing estimated lumped element values of the inductive, capacitive, and resistive elements as distributed line inductance, capacitance, and resistance respectively, and also provides for implementing the distributed line inductance, capacitance, and resistance using printed-circuit coils, transmission-line sections, and/or microstrip sections.
According to another embodiment, the present invention also provides a method of designing a transmission filter having low reflectivity and Gaussian characteristics in which the transmission line filter includes a number of half cells, each half cell having an inductive element aligned along the transmission line, and a shunt branch off of the transmission line, the shunt branch having a capacitive and a resistive element in series. The method includes generating a lumped element model of the transmission line filter, estimating lumped element values for the inductive, capacitive, and resistive elements, and approximating the lumped element values using distributed inductance, capacitance, and resistance. The distributed inductance, capacitance, and resistance are then implemented using one of printed-circuit coils, transmission-line sections, and microstrip sections.